A326117 - OEIS

%I #10 Apr 11 2021 23:51:20

%S 1,2,3,5,9,17,29,57,101,201,365,729,1233,2465,4593,8297,15921,31841,

%T 55953,111905,195713,362337,697361,1394721,2334113,4668225,9095393,

%U 17225313,31242785,62485569,106668609,213337217,392606529,755131841,1491146913,2727555425,4947175713

%N Number of subsets of {1..n} containing no products of two or more distinct elements.

%C If this sequence counts product-free sets, A326081 counts product-closed sets.

%H Fausto A. C. Cariboni, <a href="/A326117/b326117.txt">Table of n, a(n) for n = 0..47</a>

%F For n > 0, a(n) = A326116(n) + 1.

%e The a(6) = 28 sets:

%e   {}  {1}  {2,3}  {2,3,4}  {2,3,4,5}

%e       {2}  {2,4}  {2,3,5}  {2,4,5,6}

%e       {3}  {2,5}  {2,4,5}  {3,4,5,6}

%e       {4}  {2,6}  {2,4,6}

%e       {5}  {3,4}  {2,5,6}

%e       {6}  {3,5}  {3,4,5}

%e            {3,6}  {3,4,6}

%e            {4,5}  {3,5,6}

%e            {4,6}  {4,5,6}

%e            {5,6}

%t Table[Length[Select[Subsets[Range[n]],Intersection[#,Select[Times@@@Subsets[#,{2}],#<=n&]]=={}&]],{n,0,20}]

%Y Cf. A007865, A051026, A103580, A196724, A326020, A326023, A326076, A326078, A326079, A326081, A326116, A308542.

%K nonn

%O 0,2

%A _Gus Wiseman_, Jun 06 2019

%E Terms a(21)-a(36) from _Andrew Howroyd_, Aug 30 2019